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Large finite point sets have four collinear points or a visible six-clique

Lax570090.MainTheorem · concepts/Lax570090/MainTheorem.lean · lax-570090

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    Natural Language Statement

    Theorem

    Every finite set of at least 10(2450)10^(2^450) points in the real plane contains four distinct collinear points or six distinct points that pairwise see one another with respect to the whole set.

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    1import Lax570090.Geometry
    2
    3/-!
    4---
    5title: Large finite point sets have four collinear points or a visible six-clique
    6type: theorem
    7---
    8Every finite set of at least `10^(2^450)` points in the real plane contains
    9four distinct collinear points or six distinct points that pairwise see one
    10another with respect to the whole set.
    11-/
    12
    13namespace Lax570090.MainTheorem
    14
    15open Lax570090.Geometry
    16
    17axiom large_point_set_four_collinear_or_visible_six
    18 (P : Finset Point) (hP : 10 ^ (2 ^ 450) ≤ P.card) :
    19 HasFourCollinear P ∨ HasVisibleClique P 6
    20
    21end Lax570090.MainTheorem
    22
    Show Proof
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